Problem: The grades on a history midterm at Springer are normally distributed with $\mu = 79$ and $\sigma = 3.5$. Emily earned a n $89$ on the exam. Find the z-score for Emily's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Emily's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{89 - {79}}{{3.5}}} $ ${ z \approx 2.86}$ The z-score is $2.86$. In other words, Emily's score was $2.86$ standard deviations above the mean.